Periodic Event-triggering Research Articles

Periodic event-triggered data-driven control for networked control systems with time-varying delays

This article focuses on data-driven analysis and controller design for networked control systems (NCSs) with network-induced delays. The study considers a linear time-invariant (LTI) system controlled through a periodic event-triggering mechanism. First, by leveraging data-based representations, we establish data-based stability conditions for NCSs with time-varying delays. Furthermore, we propose the data-based method for co-designing the controller and the periodic event-triggering scheme. In addition, we present novel data-based conditions for verifying dissipativity properties of NCSs. The effectiveness of our proposed methods is validated through a simulation and a turbofan engine hardware-in-the-loop (HIL) experiment.

Periodic event-triggered adaptive neural control of USVs under replay attacks

This work aims to address the control issue of unmanned surface vehicles (USVs) under replay attacks, where the influence of internal/external uncertainties and actuator’s physical constraints are taken into account. In the control design, a hyperbolic tangent function is used to replace the actuator saturation nonlinearity. To solve the design problem of mismatched unknown time-varying control gain caused by replay attacks, the single-parameter-learning technique is introduced, which avoids the operation of estimating for the unknown gain directly. To compensate for the effect of lumped uncertainties including attacks, unknown dynamics and external disturbances, the adaptive neural network with the finite covering principle is involved in the kinematic and dynamic channels, respectively. Furthermore, to reduce the update rate of actuator and alleviate the actuator wear, a periodic event-triggering mechanism (PETM) is established in the controller-actuator (C-A) channel. Finally, a periodic event-triggered (PET) adaptive neural tracking control solution for USVs under replay attacks is proposed, and it is verified that the control solution can force the trajectory of USVs to follow the reference trajectory even if there exists the effect of replay attacks. In addition, all signals in the closed-loop control system of USVs under replay attacks are bounded, and simulation and comparison results demonstrate the effectiveness of the control strategy.

Dynamic periodic event-triggered control for nonlinear systems with output dynamic quantization

This paper is concerned with the design of stabilizing event-triggered controllers for nonlinear systems subject to dynamic quantization. The plant state is assumed to be partially known, and the feedback signal is transmitted to the controller at discrete-time instants via a digital channel. To that end, an event-triggered controller is synthesized based solely on the available plant measurement. In addition, to better adapt it to practical implementation, the event-triggering law we construct is only verified at periodic time instants, i.e., periodic event-triggering mechanism. Since the network is digital, the transmitted output signal must be quantized to be encoded using a finite number of bits. Furthermore, the initial output value is assumed to be unknown, and the plant is affected by external disturbance, which can result in quantizer saturation. To overcome these challenges, a dynamic quantization policy is developed for the output measurement such that the quantization regions are dynamically updated according to the value of the quantized signal. The combined approach of periodic event-triggering mechanism and dynamic quantization ensures the stability of the networked control system under mild conditions. The stability is studied using appropriate Lyapunov functions. Numerical simulations have been conducted to justify the proposed technique.

Distributed periodic event-triggered secondary control for islanded microgrids with switching topologies and communication delays

With the application of distributed generators (DGs), microgrids (MGs) have gained much attention. Combined with the distributed communication of networked systems, we investigates the secondary restoration problem in islanded microgrids. The periodic event-triggered (PET) controllers are designed for voltage restoration and frequency restoration with accurate active power allocation, which can naturally avoid Zeno behavior. By means of a common Lyapunov function, a PET protocol is designed that requires only the information of neighbors for event detection. Both event-checking sampling period and event trigger parameter are taken into account to reduce computation and communication redundancy by choosing appropriate parameters. Furthermore, considering the effect of communication delay, sufficient conditions are given to accomplish the secondary control objectives with allowable delays. Switching topologies are considered in an extra discussion. Finally, the effectiveness of the proposed PET control strategies is verified by several MATLAB simulations.

Periodic Event-Triggered Model Predictive Control for Networked Nonlinear Uncertain Systems With Disturbances.

This article investigates the event-triggered model predictive control (MPC) problem for a class of networked nonlinear uncertain systems subject to time-varying disturbances. Different from the traditional MPC, the proposed periodic event-triggered MPC (PETMPC) method does not generate new control sequence unless a predesigned periodic event-triggering mechanism (PETM) is violated. First, a generalized proportional-integral observer (GPIO) is developed to estimate the unknown state and disturbance information by using the sampled-data output of controlled system. Then, the disturbance predictions for future finite steps are obtained based on forward Euler method. After that, with the help of prediction model, the optimal control sequence, including the future finite step predicted control inputs, is generated and dexterously exploited during the interevent interval by storing it in a buffer installed between the control sequence generator and actuator, thereby leading to the further reduction of signal transmission number and the frequency of control sequence computations. Through a rigorous stability analysis, it can be proved that the closed-loop hybrid control system is globally bounded stable under the nominal PETMPC law. Finally, numerical simulations are conducted to substantiate the feasibility and superiority of the proposed PETMPC method.

Dynamic Periodic Event-Triggered Control for Networked Control Systems Under Packet Dropouts

This article presents a co-design method of dynamic periodic event-triggering mechanism (DPETM) and output-based control law for networked control systems (NCSs) subject to inevitable imperfections such as limited network resources, exogenous disturbances and successive packet dropouts. The developed DPETM has the potential to make full use of scarce network resources compared to the periodic sampled-data control on the one hand, and is natural for practical digital platforms instead of a discretized version of continuous event-triggered control (CETC) one the other hand. In this paper, the whole closed-loop system is modeled a unified hybrid system by incorporating bilateral DPETM, successive packet dropouts effects and external disturbances, and an improved hybrid Lyapunov function is constructed for stability analysis. Based on the hybrid framework, some sufficient conditions are presented to guarantee <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal{L}_2$</tex-math> </inline-formula> -stability of the system while tolerating a maximum allowable number of successive packet dropouts (MANSD). Furthermore, new linear matrix inequality (LMI) conditions for co-design of control law and triggering strategy are derived by introducing some constraints with the free variables and a modified Young’s inequality. In addition, this paper considers two scenarios relating to whether an acknowledgment scheme is employed or not. Finally, the effectiveness of the proposed method is verified by two illustrated examples and comparative studies. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —With the increasing requirement for reducing unnecessary waste of communication resources in modern industries, it is necessary to consider an alternative paradigm of the time-triggered control. In many digital control applications such as smart power grid, vehicle and remote surgery, the control tasks are often executed periodically, which makes it difficult for the theoretical results of CETC to be directly applied to practical digital platforms. The DPETM proposed in this paper, which only verifies the triggering conditions periodically at each sampling instant, is more suitable for practical digital platforms such as time-sliced embedded architectures compared to CETC. This paper investigates the stability problem for NCSs with DPETM subject to packet dropouts. Different from most of the existing literature on randomness of packet loss, this paper focuses on impact of the continuity of packet dropouts on system performance. Based on the hybrid framework and the Lyapunov approach, a co-design methodology of triggering condition and control law is proposed to ensure that the system satisfies the desired performance and can admit a MANSD.

Event-triggered output feedback control design for polynomial fuzzy systems

This paper presents a novel approach to event-triggered output feedback control of polynomial fuzzy systems that exhibit unmeasurable system states. To stabilize the system state, a fuzzy model-based event-triggered control scheme is proposed based on output measurement information. The transmission frequency is modulated using a periodic event-trigger protocol, which is scheduled by resorting to a set of historically released packets to ensure better dynamic performance. The event-triggering condition uses the current samples to determine the next trigger and also takes into account the triggering time-dependent gain parameter, thereby significantly reducing network burden. The proposed approach ensures the existence of both polynomial controller gain and event-triggered parameters by satisfying sufficient conditions based on the sum-of-squares approach and the polynomial fitting approximation algorithm. The addressed system’s stability conditions are solved using MATLAB SOSTOOLS. Three numerical examples, including an invented pendulum model, illustrate the superiority and applicability of the methodology. The main contributions of this work are the introduction of a triggering instant dependent periodic event-triggered output feedback control design, which reduces network traffic and enhances dynamic performance. The approach is validated through numerical examples, which demonstrate its superiority and applicability.

Periodic event-based sliding mode tracking control of Euler–Lagrange systems with dynamic triggering

In this article, we propose the design of a robust tracking controller of perturbed Euler–Lagrange systems (ELSs) based on dynamic event-triggered (DET) sliding mode control (SMC) with periodic evaluation of triggering rule. To ensure robustness, we employ the SMC technique and introduce a dynamic periodic event-triggering strategy to reduce communication frequency significantly. This strategy involves the incorporation of an auxiliary dynamic variable to formulate the event-triggering condition, leading to the generation of sparser triggering instants. An upper bound of the sampling period is also obtained in this design to facilitate the periodic assessment of the event-triggered strategy, alleviating the need for continuous verification of the event condition. This technique is more economical with respect to communication resources and practical than its continuous counterpart due to the relaxation of continuous measurements. The stability of the closed loop system is established using Lyapunov analysis within the dynamically triggered event-based SMC framework. The necessary switching gain for maintaining the stable motion of the sliding variable is derived with the help of Lyapunov analysis. The tracking error is shown to be ultimately bounded, and Zeno-behaviour is excluded to ensure finite sampling. A comparative analysis based on simulation results is included to highlight the effectiveness of the proposed scheme, especially in reducing the network usage in the transient phase of the response while achieving comparable steady-state behaviour. Ultimately, we validate the effectiveness of the proposed algorithm by simulating a two-link manipulator and experimentally implementing it with a one-link manipulator.

Periodic Event-Triggered MPC for Continuous-Time Nonlinear Systems With Bounded Disturbances

This paper is concerned with periodic event-triggering laws in robust model predictive control (MPC) for continuous-time constrained nonlinear systems. The online optimal control problem solved at triggering times is introduced. A periodic static event-triggering condition, in which a fixed sampling time interval plays an important role in avoiding Zeno behavior, is presented to alleviate continuous checking of event detections. Then a periodic dynamic event-triggering condition is investigated to further enlarge the minimal inter-execution time. Single-mode MPC with a prediction horizon larger than the control one is considered. Sufficient conditions of recursive feasibility for the online optimal control problem are derived. In order to relax the sufficient condition of stability, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ultimately Boundedness</i> properties are utilized in stability analysis. Finally, numerical simulation is provided to demonstrate the effectiveness of the proposed methods.

A hybrid framework of dynamic periodic event-triggered networked control systems subject to time-varying delays

This paper investigates the dynamic output-feedback control for networked control systems (NCSs). The data transmissions in the sensor-to-controller and the controller-to-actuator channels are generated by the dynamic periodic event-triggering mechanism. Due to the existence of time-varying delays in the two channels, the updated data is received after a time delay. To cope with this problem, a hybrid dynamical framework of the NCSs is established. With the help of Lyapunov function-based approach, a new event-triggering condition is designed and sufficient conditions on input-to-state stability are derived. By introducing an auxiliary function, the obtained sufficient conditions are transformed into linear matrix inequalities and the explicit forms of the dynamic output-feedback controller gains are provided. Moreover, the upper bounds on the maximum allowable transfer intervals and the maximum allowable delays are derived. Finally, a numerical example illustrates the feasibility of the proposed method.

Adaptive Neural Coordinated Control for Multiple Euler-Lagrange Systems With Periodic Event-Triggered Sampling.

This article addresses the event-triggered coordinated control problem for multiple Euler-Lagrange systems subject to parameter uncertainties and external disturbances. Based on the event-triggered technique, a distributed coordinated control scheme is first proposed, where the neural network-based estimation method is incorporated to compensate for parameter uncertainties. Then, an input-based continuous event-triggered (CET) mechanism is developed to schedule the triggering instants, which ensures that the control command is activated only when some specific events occur. After that, by analyzing the possible finite-time escape behavior of the triggering function, the real-time data sampling and event monitoring requirement in the CET strategy is tactfully ruled out, and the CET policy is further transformed into a periodic event-triggered (PET) one. In doing so, each agent only needs to monitor the triggering function at the preset periodic sampling instants, and accordingly, frequent control updating is further relieved. Besides, a parameter selection criterion is provided to specify the relationship between the control performance and the sampling period. Finally, a numerical example of attitude synchronization for multiple satellites is performed to show the effectiveness and superiority of the proposed coordinated control scheme.

Output Synchronization of Linear Heterogeneous Multi-Agent Systems With Periodic Event-Triggered Output Communication

This paper addresses an event-triggered output synchronization problem of linear heterogeneous multi-agent systems (MASs) under directed graphs, where only the outputs not the internal information of the agents are allowed to be transmitted in the network. The event-triggered output synchronization problem is divided into two subproblems, the event-triggered consensus problem of a group of reference systems and the sampled-data output regulation problem of the local agent viewing its reference system as the exosystem. Under the intermittent output communication, these two subproblems are coupled with each other and need to be solved concurrently. By an event-triggered control law with a periodic ETM, cyclic small gain conditions are derived to guarantee the event-triggered output synchronization of the linear heterogeneous MASs. Two simulation examples presented finally show the effectiveness of the theoretical results.

Periodic event-triggered dynamic output feedback control for networked control systems subject to packet dropouts

This paper proposes a co-design method of dynamic output feedback control law and periodic event-triggered control (PETC) strategy to tolerate a maximum allowable number of successive packet dropouts (MANSDs) in networked control systems (NCSs). For the purpose of striking a balance between saving limited communication resources and reducing complexity of the transmission implementation, we present the periodic event-triggering mechanism (PETM), in which the triggering conditions only needs to be monitored at each event-verifying instant. In NCSs, packets often suffer from some interference in network transmission, such as packet losses. For packet dropouts, we introduce a dropout variable and model the whole closed-loop systems as a hybrid system. Furthermore, some stability conditions for co-design are given by a novel Lyapunov function and stability theorems of hybrid systems, and the explicit designs parameters of controller and triggering conditions are presented to ensure L2 stability. Finally, two illustrated examples are given to show the effectiveness of the proposed design methods.

Approximate Optimal Control for Nonlinear Systems With Periodic Event-Triggered Mechanism.

This article investigates the approximate optimal control problem for nonlinear affine systems under the periodic event triggered control (PETC) strategy. In terms of optimal control, a theoretical comparison of continuous control, traditional event-based control (ETC), and PETC from the perspective of stability convergence, concluding that PETC does not significantly affect the convergence rate than ETC. It is the first time to present PETC for optimal control target of nonlinear systems. A critic network is introduced to approximate the optimal value function based on the idea of reinforcement learning (RL). It is proven that the discrete updating time series from PETC can also be utilized to determine the updating time of the learning network. In this way, the gradient-based weight estimation for continuous systems is developed in discrete form. Then, the uniformly ultimately bounded (UUB) condition of controlled systems is analyzed to ensure the stability of the designed method. Finally, two illustrative examples are given to show the effectiveness of the method.

Delayed impulsive stabilisation of discrete-time systems: a periodic event-triggering algorithm

This paper studies the problem of event-triggered impulsive control for discrete-time systems. A novel periodic event-triggering scheme with two tunable parameters is presented to determine the moments of updating impulsive control signals which are called event times. Sufficient conditions are established to guarantee asymptotic stability of the resulting impulsive systems. It is worth mentioning that the event times are different from the impulse times, that is, the control signals are updated at each event time but the actuator performs the impulsive control tasks at a later time due to time delays. The effectiveness of our theoretical result with the proposed scheme is illustrated by three examples.

Dynamic Periodic Event-Triggered Consensus Protocols for Linear Multiagent Systems With Network Delay

In this article, we investigate the event-triggered consensus problem for general linear multiagent systems with bounded communication network delay. To reduce the communication frequency, we propose some dynamic periodic event-triggering strategies, under which an auxiliary dynamic variable and a weighting parameter are introduced for each agent to build its event-triggering condition. Then, a distributed adaptive consensus protocol, which includes a time-varying coupling weight for each edge, is designed based on the proposed event-triggering strategies. With the well-designed updating laws of dynamic variables, coupling weights and weighting parameters, we can theoretically guarantee the consensus of the concerned multiagent systems. Our event-triggering strategies do not require agents to continuously verify the event-triggering conditions or read their neighbors’ real-time state information. Moreover, Zeno behavior is inherently excluded as the interevent intervals are bounded from below by one period in the periodic event-triggering framework. Two numerical examples are provided to verify the effectiveness of the proposed event-triggered consensus protocols.

Semiglobal Periodic Event-Triggered Output Regulation for Nonlinear Multiagent Systems

This study focuses on periodic event-triggered (PET) cooperative output regulation problem for a class of nonlinear multiagent systems. The key feature of PET mechanism is that event-triggered conditions are required to be monitored only periodically. This approach is beneficial for Zeno behavior exclusion and saving of battery energy of onboard sensors. At first, new PET distributed observers are proposed to estimate the leader information. We show that the estimation error converges to zero exponentially with a known convergence rate under asynchronous PET communication. Second, a novel PET output feedback controller is designed for the underlying strict feedback nonlinear multiagent systems. Based on a state transformation technique and a local PET state observer, the cooperative semiglobal output regulation problem can be solved by the proposed new control design technique. Simulation results of multiple Lorenz systems illustrate that the developed control scheme is effective.

Observer-based Periodic Event-triggered Boundary Control of the One-phase Stefan Problem

The Stefan problem models the phenomenon of phase transition between a liquid and a solid as the time evolution of the temperature profile of a liquid-solid material and its moving interface. This paper provides a novel observer-based periodic event-triggered boundary control (PETBC) strategy for the one-phase Stefan problem using the position and velocity measurements of the moving interface. We propose a method to convert a specific class of continuous-time dynamic event-triggers that require continuous monitoring to periodic event-triggers that only require periodic evaluation. We achieve this result by finding an upper bound on the underlying continuous-time event-trigger between two successive periodic evaluations. We provide an explicit criterion for choosing a sampling period for periodically evaluating the event-trigger. The control input is updated only at events indicated by the periodic event-trigger and is applied in a zero-order hold fashion between two events. We establish the closed-loop system well-posedness along with certain model validity conditions under the proposed PETBC. Further, we prove that the exponential convergence to the setpoint under continuous-time event-triggered boundary control (CETBC) is preserved under the proposed PETBC. We provide simulation results to validate the theoretical developments.

Dual periodic event-triggered control for multi-agent systems with input saturation

This paper is concerned with the periodic event-triggered consensus of multi-agent systems subject to input saturation. Due to the nonlinearity caused by the input saturation constraint, the accuracy of the event-triggered mechanism to screen data will be reduced. To deal with this problem, a novel dual periodic event-triggered mechanism is first proposed, in which a saturation-assisted periodic event-trigger and a complemental periodic event-trigger work synergistically to screen data more efficiently under the input saturation constraint. In addition, considering the various disturbances in the environment, a more general mixed H∞ and passive performance is introduced to describe the disturbance attenuation level. Based on the Lyapunov–Krasovskii functional, some less conservative consensus criteria are obtained for the multi-agent systems. In addition, under different input saturation constraints, the relationship between the disturbance attenuation level and the data transmission rate is explored. After that, a particle swarm optimization algorithm is a first attempt to estimate and enlarge the region of asymptotic consensus. Finally, an example is given to verify the effectiveness and superiority of our proposed method.

Event-Triggered Stabilizing Bit Rate Conditions for an n-Dimensional Linear System With i.i.d. Feedback Dropouts.

This article aims to stabilize an n -dimensional linear time-invariant (LTI) system, whose feedback packets are transmitted through a digital communication network. The digital network suffers from network delay and independent and identically distributed (i.i.d.) feedback dropouts, which may destabilize the system. The coupling among multiple state variables may further harm the stability of the system. In order to deal with these issues and save the occupied bandwidth of the feedback network, we propose a periodic event-triggering strategy. In our strategy, the state is measured periodically, but only quantized and transmitted when a certain condition is triggered. By well balancing the state coupling and making full use of both the information inside transmitted feedback packets and the one carried by sampling time instants, our strategy can maintain the desired mean square stability at a lower bit rate than conventional periodic sampling policies. The obtained stabilizing bit rate conditions are determined by the processing and network delays, the dropout rate, and the unstable eigenvalues of the system matrix, but independent of the process noise. Moreover, the lack of the direct state access does not incur any additional stabilizing bit rate. Simulations are done to confirm the effectiveness of the obtained stabilizing bit rate conditions.